The non-linear dynamic response of the euler-bernoulli beam with an arbitrary number of switching cracks

S. Caddemi (1) , I. Caliò (1) , M. Marletta (1)

1 Dipartimento di Ingegneria Civile e Ambientale

In this study the nonlinear dynamic response of the Euler-Bernoulli beam in presence of multiple concentrated switching cracks (i.e. cracks that are either fully open or fully closed) is addressed. The overall behaviour of such a beam is non-linear due to the opening and closing of the cracks during the dynamic response, however it can be regarded as a sequence of linear phases each of them characterised by different number and positions of the cracks in open state. In the paper the nonlinear response of the beam with switching cracks is evaluated by determining the exact modal properties of the beam in each linear phase and evaluating the corresponding time history linear response through modal superposition analysis. Appropriate initial conditions at the instant of transition between two successive linear phase have been considered and an energy control has been enforced with the aim of establishing the minimum number of linear modes that must be taken into account in order to obtain accurate results. Some numerical applications are presented in order to illustrate the efficiency of the proposed approach for the evaluation of the nonlinear dynamic response of beams with multiple switching cracks. In particular, the behaviour under different boundary conditions both for harmonic loading and free vibrations has been investigated.

Mots clés: Euler-Bernoulli beam; Non-linear dynamic response; Damaged beams; Switching cracks; Breathing cracks; Closing cracks; Modal analysis

S. Caddemi, I. Caliò, M. Marletta. The non-linear dynamic response of the euler-bernoulli beam with an arbitrary number of switching cracks. International Journal of Non-Linear Mechanics, 2010, 45 (7), pp.714. ⟨10.1016/j.ijnonlinmec.2010.05.001⟩. ⟨hal-00654488⟩